I encountered something similar on my W530. It's a workstation-class laptop, which means high peak power... It's designed to only work with 135W and 170W chargers. It will charge the battery from a 65W or 90W charger, but it won't run on one.
I have a lot of old 90W power supplies scattered around so I modded mine to always think it has a 135W supply connected. It works fine as long as I don't run all cores and the GPU at max power while also charging (and even then it degrades to just hiccuping until the load decreases, which is okay as long as you don't do it too much).
The magic resistor values are:
65W = 10K ohm
90W = open
135W = 0 ohm
170W = 1.5K ohm
Edit: I am not sure about the resistor values, double check this before you do it